I do not know what equipment is hard wired in your rig but we had two small portables, a batwing with the power panel and a black box similar to the one shown in the link;
Black BoxHere is a different model,
TV BoxMine is smaller and only has three inputs and three outputs.
We had a VCR and an external connection for cable.
With the Black Box, I could select OTA antenna, park cable or VCR for an input and send the signal to the record connection of the VCR, to the front or rear TV. Now part but not all of that is done by the TV by using the Input Menu of the TV. What it won't do is switch between the cable and OTA unless the cables run to each TV set. Each input cable, OTA antenna, Park cable and most likely now a DVD player requires a cable be connected to the back of the TV set. Most TVs only have one RF input(F connector) and multiple HDMI inputs. I'm sure some RVs have multiple cables prewired, it is just that I don't look at high end units but come Sept. I'll look closer at the entertainment equipment in the rigs at Pomona.
Look for the entertainment select box like the Winegard shown in the clicky and make sure it is set correctly.
I hope you can understand what I'm trying to say. Somewhere I have a line drawing of the setup but can't find it right now.